
zcgesv.f(3) LAPACK zcgesv.f(3)
NAME
zcgesv.f 
SYNOPSIS
Functions/Subroutines
subroutine zcgesv (N, NRHS, A, LDA, IPIV, B, LDB, X, LDX, WORK, SWORK, RWORK, ITER, INFO)
ZCGESV computes the solution to system of linear equations A * X = B for GE matrices
(mixed precision with iterative refinement)
Function/Subroutine Documentation
subroutine zcgesv (integerN, integerNRHS, complex*16, dimension( lda, * )A, integerLDA,
integer, dimension( * )IPIV, complex*16, dimension( ldb, * )B, integerLDB, complex*16,
dimension( ldx, * )X, integerLDX, complex*16, dimension( n, * )WORK, complex, dimension( *
)SWORK, double precision, dimension( * )RWORK, integerITER, integerINFO)
ZCGESV computes the solution to system of linear equations A * X = B for GE matrices
(mixed precision with iterative refinement)
Purpose:
ZCGESV computes the solution to a complex system of linear equations
A * X = B,
where A is an NbyN matrix and X and B are NbyNRHS matrices.
ZCGESV first attempts to factorize the matrix in COMPLEX and use this
factorization within an iterative refinement procedure to produce a
solution with COMPLEX*16 normwise backward error quality (see below).
If the approach fails the method switches to a COMPLEX*16
factorization and solve.
The iterative refinement is not going to be a winning strategy if
the ratio COMPLEX performance over COMPLEX*16 performance is too
small. A reasonable strategy should take the number of righthand
sides and the size of the matrix into account. This might be done
with a call to ILAENV in the future. Up to now, we always try
iterative refinement.
The iterative refinement process is stopped if
ITER > ITERMAX
or for all the RHS we have:
RNRM < SQRT(N)*XNRM*ANRM*EPS*BWDMAX
where
o ITER is the number of the current iteration in the iterative
refinement process
o RNRM is the infinitynorm of the residual
o XNRM is the infinitynorm of the solution
o ANRM is the infinityoperatornorm of the matrix A
o EPS is the machine epsilon returned by DLAMCH('Epsilon')
The value ITERMAX and BWDMAX are fixed to 30 and 1.0D+00
respectively.
Parameters:
N
N is INTEGER
The number of linear equations, i.e., the order of the
matrix A. N >= 0.
NRHS
NRHS is INTEGER
The number of right hand sides, i.e., the number of columns
of the matrix B. NRHS >= 0.
A
A is COMPLEX*16 array,
dimension (LDA,N)
On entry, the NbyN coefficient matrix A.
On exit, if iterative refinement has been successfully used
(INFO.EQ.0 and ITER.GE.0, see description below), then A is
unchanged, if double precision factorization has been used
(INFO.EQ.0 and ITER.LT.0, see description below), then the
array A contains the factors L and U from the factorization
A = P*L*U; the unit diagonal elements of L are not stored.
LDA
LDA is INTEGER
The leading dimension of the array A. LDA >= max(1,N).
IPIV
IPIV is INTEGER array, dimension (N)
The pivot indices that define the permutation matrix P;
row i of the matrix was interchanged with row IPIV(i).
Corresponds either to the single precision factorization
(if INFO.EQ.0 and ITER.GE.0) or the double precision
factorization (if INFO.EQ.0 and ITER.LT.0).
B
B is COMPLEX*16 array, dimension (LDB,NRHS)
The NbyNRHS right hand side matrix B.
LDB
LDB is INTEGER
The leading dimension of the array B. LDB >= max(1,N).
X
X is COMPLEX*16 array, dimension (LDX,NRHS)
If INFO = 0, the NbyNRHS solution matrix X.
LDX
LDX is INTEGER
The leading dimension of the array X. LDX >= max(1,N).
WORK
WORK is COMPLEX*16 array, dimension (N*NRHS)
This array is used to hold the residual vectors.
SWORK
SWORK is COMPLEX array, dimension (N*(N+NRHS))
This array is used to use the single precision matrix and the
righthand sides or solutions in single precision.
RWORK
RWORK is DOUBLE PRECISION array, dimension (N)
ITER
ITER is INTEGER
< 0: iterative refinement has failed, COMPLEX*16
factorization has been performed
1 : the routine fell back to full precision for
implementation or machinespecific reasons
2 : narrowing the precision induced an overflow,
the routine fell back to full precision
3 : failure of CGETRF
31: stop the iterative refinement after the 30th
iterations
> 0: iterative refinement has been sucessfully used.
Returns the number of iterations
INFO
INFO is INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
> 0: if INFO = i, U(i,i) computed in COMPLEX*16 is exactly
zero. The factorization has been completed, but the
factor U is exactly singular, so the solution
could not be computed.
Author:
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.
Date:
November 2011
Definition at line 201 of file zcgesv.f.
Author
Generated automatically by Doxygen for LAPACK from the source code.
Version 3.4.2 Tue Sep 25 2012 zcgesv.f(3) 
